Two cars possessing unequal masses are equipped with similar tyres....

Let the mass of the car be $m$ and its initial speed be $u$.

The maximum frictional force acting on the car when brakes are applied is $f = \mu N = \mu m g$, where $\mu$ is the coefficient of friction between the tyres and the road.

The deceleration of the car is $a = \dfrac{f}{m} = \dfrac{\mu m g}{m} = \mu g$.

Using the third equation of motion, $v^2 = u^2 - 2as$. For the minimum stopping distance $s$, the final velocity $v = 0$.

$0 = u^2 - 2(\mu g)s$

$s = \dfrac{u^2}{2\mu g}$

Since both cars have similar tyres, the coefficient of friction $\mu$ is the same. They also have identical initial speeds $u$.

The stopping distance $s$ is independent of the mass $m$ of the car. Thus, it is identical for both cars.